Internal Conflict-Free Projection Sets
Projections into free monoids are one of possible ways of describing finite traces. That approach is used to expand them to infinite traces, which are defined as members of a proper subfamily of cartesian product of mentioned free monoids, completed with least upper bounds in the Scott’s sense. Elements of the cartesian product are called projection sets and elements of the proper subfamily are called reconstructible projection sets. The proposed description gives useful methods of investigation. Especially, it contains a constructive operation that turns an arbitrary element of cartesian product to the closest trace. Then, we define constructively a proper subclass of projection sets, called internal conflict-free projection sets, and show using structural induction that it is precisely equal to subfamily of reconstructible projection sets. This is the main result of the paper. The proofs are ommited becouse of the page limit.
Keywordsprojection sets free monoids structural induction finite traces
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